Vowels and Fundamental Frequency

4.1 Fundamental Frequency, First Formant and “Grade”

of Vowels

According to prevailing theory, vowel­specific formant patterns are in-dependent of the fundamental frequency of their respective individual sounds.

In general, the frequencies of the first formant of all vowels, as speci-fied in current formant statistics for sounds produced in citation­form words, comparable to relaxed speech, lie within the range of the possi-ble fundamental frequencies for the speakers of a given speaker group.

Concerning long German vowels, the lowest statistical values for F1 are given for / i, y, u /, medium values for /e, ø, o /, followed by values for /ɛ, ɔ / and the highest values are indicated for /a–ɑ /.

If the fundamental frequency involved in producing vowel sounds ex-ceeds the frequencies of the first formant of / i, y, u / and approaches the frequencies of the first formant of /e, ø, o /, then it is to be expect-ed that the vowels / i, y, u / become unintelligible because their first vowel­specific formant is no longer physically representable. Thus, the vowels / i, y, u / would be of a “lower grade”, that is, more restricted in their production, physical representation and intelligibility than the other vowels. The same would apply to /e, ø, o / compared to /ɛ, a, ɑ, ɔ / and to /ɛ, ɔ / compared to /a–ɑ /.

In line with prevailing theory, the possibility that the fundamental fre-quency of a vowel sound can exceed the first formant frefre-quency of a vowel quality as given in formant statistics leads to the assumption that the “grade” of vowels differs because of vowel­specific acous-tic characterisacous-tics.

However, everyday experience refutes such a generalising conclusion.

If speakers of a given speaker group produce vowel sounds, and if the fundamental frequency of these sounds exceeds the frequencies of the statistically given first formant of / i, y, u / and approaches the frequencies of the first formant of /e, ø, o /, then all of the six vowels mentioned can be produced with the same “grade” of vowel percep-tion, given speakers with correspondingly good vocal abilities. There is no general impairment of vowel perception for the sounds of / i, y, u / if the fundamental frequency exceeds statistical F1.

The same holds true—although it is less obvious in everyday utter-ances and only for good voices—for the vowels /e, ø, o / produced at fundamental frequencies higher than the statistical values of their first formant frequencies.

Speakers with excellent vocal abilities can even produce clearly intelli-gible cardinal vowels up to a fundamental frequency that corresponds to the highest statistical F1 of all vowels of the language they master.

In this context, special attention needs to be given to everyday speak-ing styles or habits that exhibit a fundamental frequency variation of one octave or more. Such styles and habits plainly reveal the sig-nificance of the problem of fundamental frequencies above statistical first­formant frequencies, confronting the prevailing acoustic theory of the vowel.

Special attention also needs to be given to utterances of stage voi-ces (in musical and straight theatre, entertainment, film, television etc.) because extensive fundamental frequency variation is one of the hall-marks of the singing and speaking voice in the context of art and en-tertainment.

Generally, with regard to a fundamental frequency range up to the maximum frequency of the first formant as given in formant statistics, no principally different “grades” of vowel perception in relation to fun-damental and first formant frequency can be experienced.

4.2 Fundamental Frequency, Spectral Envelope, Formant Pattern and “Grade” of Vowels

If the fundamental frequency of a sound increases, so too does the frequency spacing between the harmonics in the spectrum. As a con-sequence, determining the spectral envelopes and their maxima be-comes difficult. The same applies to the calculation of formant fre-quencies. According to prevailing theory, it is to be expected that the

“grade” of vowel perception is in general also dependent on the funda-mental frequency of the sounds: with regard to fundafunda-mental frequency, the expected tendency for vowel perception is: the lower, the better;

the higher, the worse.

Indeed, considering vowel sounds at higher pitches, many scholars interpret these sounds as related to a spectral undersampling of the formants.

However, one does not only have to consider a general interrelation between fundamental frequency, harmonic spectrum, spectral

enve-37 4.2 Fundamental Frequency, Spectral Envelope, Formant Pattern

and “Grade” of Vowels

lope and expected formant frequencies, but also a formant­specific role within this interrelation: depending upon given statistical frequen-cy values of vowel­specific formants, comparisons show that sounds at higher fundamental frequencies may in some cases exhibit frequen-cies and relative amplitude maxima of harmonics that correspond to the statistical formant frequencies for the vowels in question, whereas the frequencies of the harmonics of sounds at lower fundamental fre-quencies lie in between these formant frefre-quencies. For the latter, the formants are subsequently expected to appear as envelope peaks ei-ther only indistinctly or not at all, and the corresponding vowel percep-tion is expected to be impaired when compared to sounds at higher fundamental frequencies for which the frequencies of the harmonics match statistical vowel­specific formant frequencies.

Such reasoning leads to the assumption that there is not only a general but also a discontinuous relationship between the intelligibility of vowel sounds and their fundamental frequency: accordingly, vowel sounds at lower fundamental frequencies would, as a rule, be more intelligible than vowel sounds at higher frequencies, but vowel intelligibility would also depend upon the respective relationships between fundamental frequency, harmonic spectrum and vowel­specific formant patterns (as given in formant statistics).

In line with prevailing theory, the relationship between fundamental frequency, harmonic spectrum, spectral envelope and expected vowel- specific formant pattern leads to the same assumption that the

“grade” of vowels differs in relation to vowel­specific acoustic char-acteristics.

However, as explained, everyday experience refutes such a general-ised conclusion. Thus, a theory of vowels as elements of language that formulates an inherently qualitative and at the same time discontin-uous relationship between fundamental frequency and vowel percep-tion stands in contrast with the—possibly “sensapercep-tional”—characteris- “sensational”—characteris-tic of a voiced element of language being independent of pitch within the range of intelligible speech.